# Small biomnitruncatotetracontoctachoron

Small biomnitruncatotetracontoctachoron | |
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File:Small biomnitruncatotetracontoctachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sabotic |

Coxeter diagram | ad3bc4cb3da&#ze |

Elements | |

Cells | 576 rectangular frustums, 288 rectangular trapezoprisms, 192 ditrigonal prisms, 144 ditetragonal trapezoprisms, 48 great rhombicuboctahedra |

Faces | 1152+1152 isosceles trapezoids, 576+576+576 rectangles, 384 ditrigons, 288 ditetragons |

Edges | 1152+1152+1152+1152+1152 |

Vertices | 2304 |

Vertex figure | Irregular triangular tegum |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Sabotic |

Regiment | Sabotic |

Dual | Small biomnistellatotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **small biomnitruncatotetracontoctachoron** or **sabotic** is a convex isogonal polychoron that consists of 48 great rhombicuboctahedra, 144 ditetragonal trapezoprisms, 192 ditrigonal prisms, 288 rectangular trapezoprisms, and 576 rectangular frustums. 2 rectangular frustums and 1 of each of the other 4 cell types join at each vertex.

It is one of a total of four distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great disprismatoicositetricositetrachora (that is, variants of the great prismatotetracontoctachoron with single F4 symmetry). If the great disprismatoicositetricositetrachora are of the form a3b4c3d, then the lacing edges generally have length .

This polychoron can be alternated into a small omnisnub bitetracontoctachoron, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.88663.